Solve for $x$ and $y$ using elimination. ${-x+4y = 3}$ ${x-5y = -6}$
Answer: We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Add the equations together. Notice that the terms $-x$ and $x$ cancel out. $-y = -3$ $\dfrac{-y}{{-1}} = \dfrac{-3}{{-1}}$ ${y = 3}$ Now that you know ${y = 3}$ , plug it back into $\thinspace {-x+4y = 3}\thinspace$ to find $x$ ${-x + 4}{(3)}{= 3}$ $-x+12 = 3$ $-x+12{-12} = 3{-12}$ $-x = -9$ $\dfrac{-x}{{-1}} = \dfrac{-9}{{-1}}$ ${x = 9}$ You can also plug ${y = 3}$ into $\thinspace {x-5y = -6}\thinspace$ and get the same answer for $x$ : ${x - 5}{(3)}{= -6}$ ${x = 9}$